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TU Berlin

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Wissenschaftliche Mitarbeiter

Philipp Reichenbach

Lupe

Anschrift
Technische Universität Berlin
Institut für Mathematik
Sekretariat MA 3-2
Straße des 17. Juni 136
10623 Berlin
 
Büro
Raum MA 319 (3. OG)
Institut für Mathematik
 
Persönliche Homepage:
page.math.tu-berlin.de/~reichenb/
 
ORCiD
0000-0002-5722-5505

Kontakt

Sekretariat
Beate Nießen
Raum MA 318
Tel.: +49 (0)30 314 - 25771

eMail
reichenb@math.tu-berlin.de 

Telefon
+49 (0)30 314-29280
Faxgerät
+49 (0)30 314 - 25839
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Publikationen in der Arbeitsgruppe

Tensor Rank and Complexity
Citation key OR-TensorRankAndComplexity
Author Giorgio Ottaviani and Philipp Reichenbach
Year 2020
Abstract These lecture notes are intended as an introduction to several notions of tensor rank and their connections to the asymptotic complexity of matrix multiplication. The latter is studied with the exponent of matrix multiplication, which will be expressed in terms of tensor (border) rank, (border) symmetric rank and the asymptotic rank of certain tensors. We introduce the multilinear rank of a tensor as well, deal with the concept of tensor equivalence and study prehomogeneous vector spaces with the Castling transform. Moreover, we treat Apolarity Theory and use it to determine the symmetric rank (Waring rank) of some symmetric tensors.
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